Waveguide structures with cylindrical air pores forming a two-dimensional (2-D) periodic lattice in a semiconductor material are being studied for photonic bandgap applications such as spontaneous emission control and light confinement in micro-cavities. The studies have stimulated numerous determinations of the photonic crystal (PC) band spectra based on the plane-wave expansion of the electromagnetic field, showing that in the long-wavelength limit the spectrum of electromagnetic waves can be well described in the effective media approximation with an effective dielectric constant corresponding to the results of Maxwell-Garnett theory.
Optical properties of composite structures patterned with cylindrical holes or pores, for a wavelength exceeding the inter-hole spacing, can therefore be described in terms of the fill factor alone, i.e. the fraction of total volume occupied by the pores. The properties do not depend on the long-range order of the holes or their diameter, as the effect of disorder merely amounts to weak Rayleigh scattering. The effective media approach remains valid for very large contrast ratios between semiconductor and pore permittivities, and for arbitrary propagation directions of the electromagnetic waves.
Direct comparison of the calculation results based on three-dimensional (3-D) and 2-D modeling shows that the same approach can be used to describe the wave-guiding properties of multilayered structures that include patterned layers. Moreover, studies of PC-like structures with small disorder show that the Maxwell-Garnett approach remains valid even for wavelengths barely exceeding the hole spacing, so long as the optical frequency is below the lowest photonic bandgap and light scattering remains negligible.
In semiconductor lasers and amplifiers, the propagation of different optical modes is sensitive to various structural parameters such as modal gain, material gain anisotropy and mode confinement factor, giving rise to polarization sensitivity. For example, the typical three-layer waveguide design of semiconductor amplifiers with isotropic constituents results in better confinement of the TE mode and a larger gain for this mode in comparison with the TM mode. To obtain a polarization-insensitive amplifier, one had to use highly anisotropic active layers with a material gain that favors TM polarization.